Posted on 04/19/2002 6:03:12 AM PDT by SJackson
Having taken control of the Senate by virtue of James Jeffords's turncoat act, the Democrats are using their one toehold on power to bring the process of government to a halt. Unable to persuade the public or even a majority of the Senate on the merits, Majority Leader Tom Daschle is devoting his energies to making sure the World's Greatest Deliberative Body takes no votes.
In particular, Mr. Daschle promises that his party will "never bring up the permanent tax cut the President has advocated." This is, of course, the same bill that the House passed yesterday by a 229-198 vote. As the President proposed, it would make permanent the tax cuts that Congress passed last year, with the heady provision that they would all expire in 2010. While this was intended to square the procedural circle Congress has inflicted on itself, someone since noticed that the 2010 expirations would constitute the biggest tax increase in the nation's history.
Mr. Daschle says making the cuts permanent "is bad policy, it is wrong, and it compounds the budget disaster that our country currently faces." He's entitled to his opinion, just as he was when he blamed last year's tax cuts for the now-vanishing recession. But why not test his proposition with a vote? Because 12 Democrats supported the tax cuts last year, and many of them would have to explain a reversal in this fall's election campaign.
These include freshman Senator Tim Johnson from Mr. Daschle's own South Dakota. Yesterday the state's lone Congressman, Republican John Thune, urged the Senator to renew his backing of the bill to welcome President Bush on an April 24 visit to the state. "I hope Tim Johnson will join me in standing by the President and continuing to support the tax cuts he voted for last summer," the Congressman said, in a taste of what the Senator can expect in the fall campaign. So to avoid either losing on the bill or losing in the elections, Mr. Daschle has to duck a vote.
On judicial nominations, similarly, Democrats on the Judiciary Committee refused to allow a floor vote on Charles Pickering Sr., even after they dropped earlier canards about racism. Incredibly enough -- or perhaps in a stroke of advance planning -- no Democratic Senator on the Committee faces re-election this fall. The Senate has approved only eight of 30 Presidential nominations to appellate courts. Three have had a hearing but no vote, while 18 have no hearing scheduled. Eight of these have been pending since last May.
Even yesterday's Daschle "victory" on oil drilling in the Arctic National Wildlife Refuge came on a procedural vote. Democrats threatened a filibuster over 2,000 acres of tundra in a vast wilderness few people ever see, but which denizens of Beverly Hills and Georgetown have adopted as a pet, or perhaps an Earth god. If the 54 against closing debate actually represented the divisions on the merits, Mr. Daschle surely would have allowed a vote on the yeas and nays.
The Democrats have also been dragging their feet on the simple housekeeping measure of an increase in the debt limit. "Why can't we stop this madness," Treasury Secretary Paul O'Neill asked at a hearing yesterday; Social Security checks will continue to go out thanks to the inpouring of income-tax revenues, but eventually the Treasury will "run out of tricks." Also yesterday, Mr. Daschle promised an increase, though he wouldn't say how much or when.
Meanwhile, Senator Kurt Conrad and his Budget Committee are struggling to produce a budget resolution, with the Democratic caucus divided between big spenders such as Bobby Byrd and Ted Kennedy, and New Democrats such as Zell Miller and John Breaux likely to move toward Republicans. Even with ANWR out of the energy bill, some Democrats are in revolt over the Daschle ethanol boondoggle. The farm bill is tied up in conference committee over big spending. And despite some passing promises, the Majority Leader continues to sit on trade-promotion authority.
With due respect for the even divisions at all levels of the last election, we somehow doubt that anyone wanted permanent deadlock. We very much doubt that when they pulled the lever for Jim Jeffords on the GOP line, Vermont voters had in mind turning the Senate over to Mr. Daschle. Voters should be asked in November whether they want more inaction and deadlock, and it's up to the Republicans and their President to frame that issue for them.
And all on freerepublic are well aware of my continuing mantra, "The US senate, is without question, the most dangerous group of powerful, power hungry, power crazed, power drunk, power mad, individuals on the face of the earth. Their true character was discovered during the non-impeachment trial of willy the worst, and they should all...."
If their is anyone within the sound of my voice, (internet speak) who does not know the senate is running nay ruining the country, let them now speak or forever hold their, peace.
The nation is at war, oil resources are a vital national interest, and the idiot midget named Dasshole thinks these politics will somehow help to Dumbocrats get some traction in the upcoming elections.
He is a certified moron.
My math is a bit rusty, but I figure the odds of that happening by accident at about 729:1 against.Since Hillary put in one grand and came out with 98, I figure the odds on The Great Cattle Futures Coup was "only" 98:1 against . . .
If you have a coin and you flip it 6 times you will have seven different possible outcomes, of various likelihoods which follow a binomial distribution. That is, you could get all heads, or all tails, or anything in between. The chanceof all heads would be one in 64,In the case of senators, there are three different classes--those due for election this year, those due for election in '04, and those due for election in '06. Glossing over the question of differences in the sizes of the Democratic contingents among the three groups, it would seem that we would have to raise not a binomial but a trinomial to the sixth power to estimate the probabilities of the various combinations. To do so I created Pascal's Triange and a vertical vector of the
of only one tail 6 in 64,
of two tails would be 15 in 64,
of three tails would be 20 in 64,
of four tails would be 15 in 64,
of five tails would be 6 in 64, and
of six tails would be one in 64.[1, 6, 15, 20, 15, 6, 1] set.
Multiplying each row of the triange by the corresponding (single-element) row of the vector yields a symmetrical triangular table whose sides, top and main diagonal replicate the 1, 6, 15, 20, 15, 6, 1 set. That, I take it, yields the coefficients of the various powers of a, b, and c which result from taking (a+b+c) to the sixth power.
The spreadsheet indicates the sum of the elements of that table to be 729. And that is my estimate of the odds against all six (do I have that number right?--it may be more, which would make this a marked underestimate of the odds) Democratic senators being chosen without reference to their next election all happening to not be up for reelection in 2002.
The most important questions of life are, for the most part, really only questions of probability. Strictly speaking, one may even say that nearly all our knowledge is problematical; and in the small number of things which we are able to know with certainty, even in the mathematical sciences themselves, induction and analogy, the principal means of discovering truth, are based on probabilities, so that the entire system of human knowledge is connected with this theory.
Pierre-Simon de Laplace (1749 - 1827) What is Probability?
Probability is the likelihood of an occurrance happening.
Probability Experiment
Process which leads to well-defined results call outcomes
Outcome
An outcome is the result of an experiment or other situation involving uncertainty.
When writing the sample space, it is highly desirable to have events which are equally likely.
Another example is rolling two dice. The sums are { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }. However, each of these aren't equally likely. The only way to get a sum 2 is to roll a 1 on both dice, but you can get a sum of 4 by rolling a 3-1, 2-2, or 3-1. The following table illustrates a better sample space for the sum obtain when rolling two dice.
First Die | Second Die | |||||
1 | 2 | 3 | 4 | 5 | 6 | |
1 | 2 | 3 | 4 | 5 | 6 | 7 |
2 | 3 | 4 | 5 | 6 | 7 | 8 |
3 | 4 | 5 | 6 | 7 | 8 | 9 |
4 | 5 | 6 | 7 | 8 | 9 | 10 |
5 | 6 | 7 | 8 | 9 | 10 | 11 |
6 | 7 | 8 | 9 | 10 | 11 | 12 |
Event
An event is any collection of outcomes of an experiment.
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Formally, any subset of the sample space is an event.
Any event which consists of a single outcome in the sample space is called an elementary or simple event. Events which consist of more than one outcome are called compound events.
Set theory is used to represent relationships among events. In general, if A and B are two events in the sample space S, then:
(A union B) = 'either A or B occurs or both occur'
(A intersection B) = 'both A and B occur'
(A is a subset of B) = 'if A occurs, so does B'
A' or = 'event A does not occur'
(the empty set) = an impossible event
S (the sample space) = an event that is certain to occur
Example
Experiment Rolling a dice once
Sample space S = {1,2,3,4,5,6}
Events A = 'score < 4' = {1,2,3}
B = 'score is even' = {2,4,6}
C = 'score is 7' =
= 'the score is < 4 or even or both' = {1,2,3,4,6}
= 'the score is < 4 and even' = {2}
A' or = 'event A does not occur' = {4,5,6}
Sum | Frequency | Relative Frequency |
2 | 1 | 1/36 |
3 | 2 | 2/36 |
4 | 3 | 3/36 |
5 | 4 | 4/36 |
6 | 5 | 5/36 |
7 | 6 | 6/36 |
8 | 5 | 5/36 |
9 | 4 | 4/36 |
10 | 3 | 3/36 |
11 | 2 | 2/36 |
12 | 1 | 1/36 |
If just the first and last columns were written, we would have a probability distribution. The relative frequency of a frequency distribution is the probability of the event occurring. This is only true, however, if the events are equally likely.
This gives us the formula for classical probability. The probability of an event occurring is the number in the event divided by the number in the sample space. Again, this is only true when the events are equally likely. A classical probability is the relative frequency of each event in the sample space when each event is equally likely.
P(E) = n(E) / n(S)
0 <= P(E) <= 1
Two events are mutually exclusive if they cannot occur at the same time. Another word that means mutually exclusive is disjoint.
If two events are disjoint, then the probability of them both occurring at the same time is 0.
Disjoint: P(A and B) = 0
If two events are mutually exclusive, then the probability of either occurring is the sum of the probabilities of each occurring.
P(A or B) = P(A) +- P(B)
Example 1:
Given: P(A) = 0.20, P(B) = 0.70, A and B are disjoint
I like to use what's called a joint probability distribution. (Since disjoint means nothing in common, joint is what they have in common -- so the values that go on the inside portion of the table are the intersections or "and"s of each pair of events). "Marginal" is another word for totals -- it's called marginal because they appear in the margins. B B' Marginal
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The values in red are given in the problem. The grand total is always 1.00. The rest of the values are obtained by addition and subtraction.
P(A or B) = P(A) +- P(B) - P(A and B)
Example 2:
Given P(A) = 0.20, P(B) = 0.70, P(A and B) = 0.15
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Interpreting the table
Certain things can be determined from the joint probability distribution. Mutually exclusive events will have a probability of zero. All inclusive events will have a zero opposite the intersection. All inclusive means that there is nothing outside of those two events: P(A or B) = 1.
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An example would be rolling a 2 on a die and flipping a head on a coin. Rolling the 2 does not affect the probability of flipping the head.
If events are independent, then the probability of them both occurring is the product of the probabilities of each occurring.
P(A and B) = P(A) * P(B)
Example 3:
P(A) = 0.20, P(B) = 0.70, A and B are independent.
B | B' | Marginal | |
A | 0.14 | 0.06 | 0.20 |
A' | 0.56 | 0.24 | 0.80 |
Marginal | 0.70 | 0.30 | 1.00 |
The 0.14 is because the probability of A and B is the probability of A times the probability of B or 0.20 * 0.70 = 0.14.
Conditional Probability
The probability of event B occurring that event A has already occurred is read "the probability of B given A" and is written: P(B|A)
P(A and B) = P(A) * P(B|A)
Example 4:
P(A) = 0.20, P(B) = 0.70, P(B|A) = 0.40
A good way to think of P(B|A) is that 40% of A is B. 40% of the 20% which was in event A is 8%, thus the intersection is 0.08.
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A and B are independent events
P(A and B) = P(A) * P(B)
P(A|B) = P(A)
P(B|A) = P(B)
The last two are because if two events are independent, the occurrence of one doesn't change the probability of the occurrence of the other. This means that the probability of B occurring, whether A has happened or not, is simply the probability of B occurring.
Equally Likely Events
Events which have the same probability of occurring.
Complement of an Event
All the events in the sample space except the given events.
P(E) = f / n
Uses a frequency distribution to determine the numerical probability. An empirical probability is a relative frequency.
Relative Frequency
Relative frequency is another term for proportion; it is the value calculated by dividing the number of times an event occurs by the total number of times an experiment is carried out. The probability of an event can be thought of as its long-run relative frequency when the experiment is carried out many times.
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Example
Experiment Tossing a fair coin 50 times n = 50
Event E = 'heads'
Result 30 heads, 20 tails r = 30
Relative frequency:
If an experiment is repeated many, many times without changing the experimental conditions, the relative frequency of any particular event will settle down to some value. The probability of the event can be defined as the limiting value of the relative frequency:
P(E) = rfn(E)
For example, in the above experiment, the relative frequency of the event 'heads' will settle down to a value of approximately 0.5 if the experiment is repeated many more times.
A subjective probability describes an individual's personal judgement about how likely a particular event is to occur. It is not based on any precise computation but is often a reasonable assessment by a knowledgeable person.
Like all probabilities, a subjective probability is conventionally expressed on a scale from 0 to 1; a rare event has a subjective probability close to 0, a very common event has a subjective probability close to 1
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A person's subjective probability of an event describes his/her degree of belief in the event.
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Personal Probability is how strongly someone feels that an event will occur.
Simple Rules to Personal Probability
Your personal probability must be between 0 and 100%
The personal probability must also be coherent, this means that a personal probability should be consistent with any other probabilities given by that person. --------------------------------------------------------------------------------
The use of personal probability in everyday life
We use personal probability all the time and probably do not realize it. If you have ever driven on the Interstate during rush hour traffic, you have probably used some personal probability to try to pick which lane will move the fastest, which alternate route to take, etc. The traffic dilemma also uses some relative frequency to help base some decisions on. Chances are you have been stuck on the freeway and have noticed patterns in movement, you can predict when it will jam and other factors. Using this information helped to make a better choice of what route to take, what lane to be in, etc.
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Calibration of Personal Probability
Calibration of personal probability is a good thing to know when making a decision using a personal probability. If I were to bet on football games, I would call a person who knows a lot about football and makes odds based on that knowledge. But I would also like to know how well their predictions come out in the real world. A oddsmaker must be fairly calibrated if they are going to stay in business. But it would be smart to pick the best calibrated oddsmaker out there to base your decisions upon.
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How do we calibrate personal probabilities?
To calibrate personal probabilities we should use the relative frequency and compare it to the probabilities that we were given.
Example
What is probability of a 4 on a die given that the die comes up even?
Note that sample space has now changed, it no longer includes {1,2,3,4,5,6}, but instead contains {2,4,6}. P(4|even) = 1/3
What is probability that a die comes up odd given that the dies is 3 less?
P(odd|3 or less) = 1/3
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Using a table conditional probabilities are easier to determine.
Dime Nickel Quarter Total
Heads 9 5 6 20
Tails 4 10 16 30
Totals 13 15 22 50
Probabilies 13/50 15/50 22/50 1
What is the probability of getting a dime and tails? P(dime and tails)? = 4/50
What is the probability of getting a dime given tails? P(dime | tail) = 4/30
What is the probability that heads will come up given nickels or quarters? P(head|nickel or quarter) = (5+-6)/(15+-22) = 11/37
Example - A family of 3 children
In a family of 3 children suppose you are told that there are fewer than 2 boys. What is the probability that all 3 children are of the same sex?
Using the previous notation
C : all children of the same sex
D : fewer than 2 boys.
We want the probability of C given that D has occurred. We will use the notation P(C|D) to describe this. Each column lists all outcomes.
Those comprising the events
C and D are in boldface. 'C' 'D'
GGG GGG
GGB GGB
GBG GBG
GBB GBB
BGG BGG
BGB BGB
BBG BBG
BBB BBB
As D has occurred, only 4 outcomes are now possible: GGG, GGB, GBG and BGG. Their probabilities must be made to sum to 1. To achieve this the probabilities calculated previously need to be "rescaled" by dividing by their total, which was P(D) = 0.47.
The probability of C, given that D has occurred, is called the conditional probability and is written as P(C|D). Recall that the probability of GGG was 0.11:
In general for events A and B the conditional probability of A given that B has occurred is
This can also be rearranged to give the useful formulas
P(A and B) = P(A|B)P(B)
P(A and B) = P(B|A) P(A)
Example - Gender of employees
The table below shows the probabilities of males (M) and females (F) being employed (E) or unemployed (U) in some population (it excludes those not wishing to be employed).
M | F | ||
E | 0.52 | 0.41 | 0.93 |
U | 0.05 | 0.02 | 0.07 |
0.57 | 0.43 | 1.00 |
Find
(a) P(E|M), the conditional probability of employment given that the person is male
(b) P(M|E), the conditional probability of being male given that the person is employed.
Answers:
Figure 3: Tree model showing conditional probabilities
e.g. P(E) = P(E and M) +- P(E and F)
= P(E|M)P(M) +- P(E|F)P(F)
= 0.91 x 0.57 +- 0.95 x 0.43 = 0.93
Suppose we have known probability of two complementary events A1 and A2, ( P(A1), P(A2) )These two events are mutually exclusive, so there probability will sum up to one. Suppose, B is another event, then the conditional probailities are P(B/A1) and P(B/A2), which are known. (These are probabilities that B happens as a sequence of A1 or A2).
The Bayes' Rule is :
P(A1|B)= [P(A1)P(B|A1)] / [P(A1)P(B|A1)+-P(A2)P(B|A2)]
Bayes' rule can be used to tell you the chances of having an illness given that the results you have recieved are positive.
Example: The probabilities of winning and the amount of winning prices for a local lottery game (where the players pick 5 numbers from 1 to 60 to try to match the 5 randomly selected winning numbers. The cost per entry is $2) are presented below: Number of Matches Price Net Gain Probability The expected value for the players then is calculated: EV=($9998*0.000015)+-($998*0.00072)+-($48*0.00143)+-($39*0.0425)+-($0*0.314)+-(-$2*0.659)=-0.25 This means that over many repetitions playing this game, the player will lose an average of 25 cents each time they play. Coincidences... When strange things happen... From a midterm we have the odds of being struck as 1/685,000. Since lightning strikes are independant, we can multiply the odds to get the odds for being struck twice(Rule 3). This turns out to be 1/469,225,000,000. This isn't very likely but you can be sure that there are people out there who have been hit twice or even more times. What does it all mean? Life is a gamble, you could get hit by lightning, the odds aren't that low. We know you are more likely to be hit by lightning than you are to win the lottery, which has a chance of 1:6,999,999 to win. So if you have learned anything, don't bet on the lottery, think of the lotto as a big Russian Roulette game, 7 million chambered revolver, all but 1 chamber is filled... Would you play? |
Let's see, the number of possible states for each senator is three:no congressional terms of cushion before the next election,There are six (perhaps more?) Democrats on the Senate Judiciary Committee. The number of seats (6) is the power to which the number of possible states (3) must be raised to determine the total number of ways the various seats could have been filled.
one congressional term of cushion before the next election, and
two congressional terms of cushion before the next election.36=729, in agreement with my previous post. However, I was wrong to suggest that only one of these combinations leaves the Democrats without a Judiciary Committee member standing for election. To the contrary, there are quite a few. To judge by my table, there are 64 of them. So the actual odds-against would be
729/64 = 11.4:1The conclusion is that the absence of a Democratic Judiciary Committeman now standing for reelection is distinctly suspicious, but not to the 98:1, "oh, come on now" level of Cattlegate.
This indicates that the odd against random selection of 6 Democratic senators not being up for reelection this year are 6.8:1. For seven Democratic senators it would by 9.7:1 . . .
But then, Teddy Kennedy wouldn't be affected in any event, so his election date would be irrelevant to his being chosen. I think however that Max Cleland would not fall into that category . . .
I see now that there are ten Democrats on the Senate Judiary committee! That is a horse of a different color; assuming that Dem Judiciary Committee members were chosen without regard to their re-election needs then:NoIt's commonplace in statistics to accept a hypothesis if there is a 5% (one in twenty) chance of error due to random chance. One chance in 29.5 may not quite be one in ninety-eight like Cattlegate, but it still is definitely in
of Dem odds
senators
1 - 10 in 13
2 - 10 in 18
3 - 10 in 25
4 - 10 in 35
5 - 10 in 49
6 - 10 in 68
7 - 10 in 97
8 - 1 in 13.9
9 - 1 in 20
10 - 1 in 29.49"Oh, come on now"territory.
And who were the knaves, those who scored a big goose egg in CCAGW's ratings? In the Senate there were four: Sens. Hillary Clinton (D-N.Y.), Kent Conrad (D-N.D.), Byron Dorgan (D-N.D.) and Barbara Mikulski (D-Md.). In the House, there were eight representatives who scored zeros: Reps. Patrick Kennedy (D-R.I.), Steven Lynch (D-Mass.), Patsy Mink (D-Hawaii), John Olver (D-Mass.), Lucille Roybal-Allard (D-Calif.), Diane Watson (D-Calif.), Robert Wexler (D-Fla.) and Lynn Woolsey (D-Calif.).
In the Senate, Republicans scored an average of 77 percent and Democrats were at 15 percent. In the Senate, Majority Leader Tom Daschle (D-S.D.) scored 5 percent, while his counterpart Minority Leader Trent Lott (R-Miss.), had a score of 80 percent. In the House, Speaker Hastert scored 100 percent, while Minority Leader Dick Gephardt (D-Mo.) scored 7 percent.
Cagw, Citizens Against Government Waste.
As long as the press/Dems. are interested in accountability and stewardship of other people's money all of a sudden...
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